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  • ENHANCED TRAILER BACKING

    By

    AMIT DAVID JAYAKARAN

    A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

    OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

    UNIVERSITY OF FLORIDA

    2004

  • Copyright 2004

    by

    Amit David Jayakaran

  • This document is dedicated to my parents.

  • iv

    ACKNOWLEDGMENTS

    I would like to express my gratitude to Dr. Carl Crane III, who as my advisor came

    up with the idea for this thesis and who guided me for the past year and a half. I would

    also like to thank Dr. David Dooner for his immense help in getting my work started and

    putting me on the right track. I would also like to thank Dr. Robert Bicker who helped me

    through the last part of my work. I would like to thank Dr. John Kenneth Schueller for

    being on my committee.

    I also owe a lot of gratitude towards Shannon Ridgeway and Dr. Carol Chesney

    who helped me at various points during my work.

    On a more personal note I would like to thank my parents and brother for their love

    and support. I would also like to thank my friends at the University of Florida who have

    directly and indirectly contributed to my work here.

  • v

    TABLE OF CONTENTS Page ACKNOWLEDGMENTS ................................................................................................. iv

    LIST OF TABLES............................................................................................................ vii

    LIST OF FIGURES ......................................................................................................... viii

    ABSTRACT...................................................................................................................... xii

    CHAPTERS

    1 INTRODUCTION ............................................................................................................1

    2 REVIEW OF LITERATURE ...........................................................................................4

    Overview.......................................................................................................................4 Definitions ....................................................................................................................5

    Jack Knifing...........................................................................................................5 Instant Center of Rotation .....................................................................................5 Radius of Turn.......................................................................................................6 Curvature of Path...................................................................................................6 Nonholonomic Constraints....................................................................................6 Small Time Controllable .......................................................................................7 Off-Hooking ..........................................................................................................7 Center of Rotation .................................................................................................8

    3 APPROACH .....................................................................................................................9

    Assumptions .................................................................................................................9 Approach.......................................................................................................................9 Stable Values of Theta................................................................................................13

    Analytical Solution for the Polygon ....................................................................13 The Simulink Model............................................................................................18

    Velocity Analysis........................................................................................................22 Stabilizing the Trailer .................................................................................................27

    4 DESIGN DESCRIPTION...............................................................................................30

    Mechanisms to Align Trailer ......................................................................................30

  • vi

    Method I ..............................................................................................................30 Method II .............................................................................................................31

    Implementation ...........................................................................................................36 Simulink ..............................................................................................................36 Physical Model ....................................................................................................38

    Data acquisition-Potentiometers ..................................................................38 The Servo .....................................................................................................42

    The Prototype..............................................................................................................43 Rotary to Linear Conversion ...............................................................................43 Mounting of Potentiometers ................................................................................46

    Trailer angle potentiometer ..........................................................................46 Steering angle potentiometer........................................................................46 x value feedback potentiometer....................................................................46

    Approximation of Sine Using Taylor Series Expansion.............................................47 Implementation ...........................................................................................................54

    5 RESULTS AND CONCLUSIONS ................................................................................55

    APPENDIX SOFTWARE MODEL OF THE TRAILER PROBLEM .............................62

    LIST OF REFERENCES...................................................................................................72

    BIOGRAPHICAL SKETCH .............................................................................................74

  • vii

    LIST OF TABLES

    Table page 4-1: Sample Values for the Setup ......................................................................................36

    4-2: High-torque Ball-bearing Servo Motor from GWS....................................................42

    4-3: Taylor Substitution .....................................................................................................48

  • viii

    LIST OF FIGURES

    Figure page 1-1: Jackknifing ...................................................................................................................1

    2-1: Instant Center of Rotation ............................................................................................6

    2-2: Center of rotation..........................................................................................................8

    3-1: Combined Instant Center............................................................................................10

    3-2: Combined Instant Center............................................................................................10

    3-3: Simplified system and the solution polygon ..............................................................11

    3-4: Solution 1 for the Angle θ ..........................................................................................12

    3-5: Solution 2 for the Angle θ ..........................................................................................12

    3-6: Calculation of the Distance of the Instant Center from the Center of the Rear Axle.14

    3-7: Trailer and Vehicle Polygon......................................................................................15

    3-8: Triangle to Help Simplify the Solution ......................................................................17

    3-10: Reading Constants - I ...............................................................................................20

    3-11: Reading Constants - II ..............................................................................................20

    3-12: Calculation of the Instant Center - I .........................................................................20

    3-13: Calculation of the Instant Center - II ........................................................................20

    3-14 Solution for First Theta Value ...................................................................................21

    3-15 Solution for Second Theta Value...............................................................................21

    3-16: Plot of Turning Radius .............................................................................................22

    3-17: The Setu